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https://docs.google.com/document/edit?id=1z_1UPP6QCU7mgZzH_QQ5KRPBqTJ7kLm1GPmENuKJiwQ&hl=en

Algebra 1: Direct Variation & Effects of Slope and Y-intercepts

Emily E - WHS

Objectives: Students will:

  • Understand direct variation and its applications to the real world.
  • Conjecture and explore about effects of slope and y-intercept.
  • Compare conjectures and exploration results.
  • Link knowledge to forms of linear functions.


NC Standard Course of Study Objectives:
  • Competency Goal 4:The learner will use relations and functions to solve problems.
    • 4.01 Use linear functions or inequalities to model and solve problems; justify results.
      1. Solve using tables, graphs, and algebraic properties.
      2. Interpret constants and coefficients in the context of the problem.

Description of Lesson: This lesson will provide students the opportunity to explore, in groups or individually, one type of linear function, direct variation. Students will also navigate the effects of slope and y-intercept on a graphical representation and compare their prior thoughts to the realities they have seen through the exploration. These thoughts will lead into the discussion of the forms of linear functions.

Materials Needed & Technologies Used
  • Student Laptops
  • Geometer’s Sketchpad
  • “Direct Variation” Premade Sketch (from slimath2.wikispaces.com)
  • “Slope and Y-Intercept Exploration”
  • SchoolFusion Website (or a wikispace page)

Outline of Lesson
  1. Begin the lesson with students working through the “Direct Variation” premade sketch independently.
  2. When students are finished with the GSP activity in #1, they need to complete the __Google Form__ as a quick assessment.
  3. After the students have completed the assessment, arrange them into pairs or small groups.
  4. The groups will designate a ‘note taker’ and a ‘post person.’
  5. They will discuss what effects they think the slope will have on the graphical representation as well as what effects the y-intercept will have on the graph and why they create their conjectures. The ‘note taker’ will write down the groups’ thoughts.
  6. The ‘post person’ will post their group’s conjectures onto the SchoolFusion blog under our class page.
  7. After the groups have posted their conjectures, they will explore the effects that changing slope and y-intercept have on a graphical representation of a linear function by using __GSP Slope and Y-Intercept Exploration file__.
  8. After they have sufficiently explored and created their own relationships, the students should compare and contrast their original conjectures with what they actually observed.
  9. Once they have developed a coherent comparison of the two thoughts, the students should create a quick presentation (powerpoint or online resource) to show their comparison. The groups will share these presentations with the class and will be graded based on the rubric at the bottom of the lesson outline.
  10. Tie the explorations from this lesson to the different forms of linear functions (slope-intercept, point-slope and standard form).


Rubric for Group Presentations:
Aspect of Presentation
 Above & Beyond
(5 points)
 On Target
(3-4 points)
 Needs Improvement (1-2 points)
Explanation of Initial & Post-Exploration Conjecture
 Thorough and complete explanations of how the thinking process occurred in the group.
Portions of explanations are missing.
 Little or no explanation of conjectures and comparison.
Thoroughly Investigated
 The presentation shows that time was used wisely to explore and think about the effects of slope and y-intercept on a graph.
 Time may not have been used productively at all times and lacks some depth to the statements.
 Time not used wisely and/or no depth of statements.
Creative
 The presentation is creative in design and communication with the class during presentation.
 The presentation lacks some creativity or effective communication.
 Little or no creativity or flow to the presentation.